The purpose of the study is to determine by the finite element method the stress-strain state and behavior of contact interaction characteristics under various loading conditions of the liner-shaft system, which is used for materials research when operating under conditions of frictional and mechanical fatigue. The cases of loading the system with different ratios of contact forces applied to the liner and bending forces applied to the shaft are considered. Verification of the results is carried out using beam theory and contact theory. According to the results of the study, it is shown that depending on the direction and magnitude of the bending load, it is possible to form a contact area of three different shapes: rectangular, elliptical, and divided into two parts. Furthermore, optimal load ratios minimizing the von Mises stresses were identified: in the liner with co-directed Fb and FN at a ratio of FN/Fb = 20–50 (e.g., at FN = 500 N, Fb = 25 N); in the shaft with oppositely directed Fb and FN at a ratio of FN/ Fb = 20 (e.g., at FN = 500 N, Fb = 25 N). Thus, the presented approach to modeling volumetric damage in a friction pair, one element of which is loaded by a non-contact force, provides an opportunity to solve optimization and damage management problems for complex technical systems by controlling boundary conditions without costly design or material changes.
Sherbakov et al. (2025) studied this question.